1. Field of the Invention
This invention relates to apparatus and a method for fast real time decoding of Nordstrom-Robinson encoded information in the presence of additive white Gaussian noise (AWGN). More particularly, the present invention relates to an exact fast maximum likelihood (ML) decoder employed in a receiver for decoding demodulated signals that were previously coded into Nordstrom-Robinson (16,256,6) non-linear code for transmission in an AWGN channel.
2. Description of the Prior Art
Heretofore, maximum likelihood (ML) decoding of Nordstrom-Robinson coded information was known. The prior art direct method of performing maximum likelihood decoding of a binary block code L in length in the presence of additive white Gaussian noise maps an arbitrary point .times. in R.sup.n onto that codeword closest in Euclidean distance. The advantage of this maximum likelihood decoding technique is a coding gain of approximately 2 db over hard decision decoding accomplished for the same code. The most direct approach to maximum likelihood decoding is to compute the Euclidean distance from the received vector x for each codeword and then to select the codeword u closest to x in Euclidean distance. The complexity of this procedure grows rapidly with the size of the code and renders the implementation of high-speed apparatus of this procedure impractical for real time decoding.
J. H. Conway and N. J. A. Sloan in their article entitled "Soft Decoding Techniques for Codes and Lattices, Including the Golay Code and the Leech Lattice", IEEE Trans. Inform. Theory, Vol. IT-28, No. 1, Pg. 41-50, January 1986 describe a general procedure for maximum likelihood decoding that can be made more efficient than the direct method procedure referred to above if the code being decoded has a subcode of small index that can itself be rapidly decoded.
It has been found that the above-mentioned Conway and Sloan procedure can be applied to maximum likelihood decoding of the non-linear extended Nordstrom-Robinson (NR) code which has an easily decoded subcode with an index 32.
It would be extremely desirable to provide decoding apparatus and a method for maximum likelihood decoding of a non-linear code employing coset leaders of a partition subcode and to reduce the complexity of the decoding procedure to enable real time decoding of a Nordstrom-Robinson Code.